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This article has been retracted as an almost identical paper by the same author has been simultaneously submitted to and published in Journal of Computational and Applied Mathematics. The other publication is “Solution of nonlinear Fredholm integro-differential equations using a hybrid of block pulse functions and normalized Bernstein polynomials,” Volume 260, April 2014, Pages 258–265, DOI: 10.1016/

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  1. S. H. Behiry, “Numerical solution of nonlinear fredholm integrodifferential equations by hybrid of block-pulse functions and normalized bernstein polynomials,” Abstract and Applied Analysis, vol. 2013, Article ID 416757, 8 pages, 2013.
Abstract and Applied Analysis
Volume 2013, Article ID 416757, 8 pages
Research Article

Numerical Solution of Nonlinear Fredholm Integrodifferential Equations by Hybrid of Block-Pulse Functions and Normalized Bernstein Polynomials

General Required Courses Department, Jeddah Community College, King Abdulaziz University, Jeddah 21589, Saudi Arabia

Received 24 April 2013; Accepted 1 September 2013

Academic Editor: Santanu Saha Ray

Copyright © 2013 S. H. Behiry. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A numerical method for solving nonlinear Fredholm integrodifferential equations is proposed. The method is based on hybrid functions approximate. The properties of hybrid of block pulse functions and orthonormal Bernstein polynomials are presented and utilized to reduce the problem to the solution of nonlinear algebraic equations. Numerical examples are introduced to illustrate the effectiveness and simplicity of the present method.